Let us first look at: matrices, selection from a matrix and selection from a vector. These elements exist in both recommendations, but differ syntactically.
Selection from a matrix and from a vector is done by the
<selector/> element in MathML and by the symbols
vector_selector and matrix_selector in OpenMath. Because
MathML uses the same element to deal both with matrices and vectors, it
is necessary for the parser to determine what the arguments of the
expression are before finding the correct equivalent OpenMath. If the
expression has a matrix as argument, then matrix_selector is the
correct corresponding symbol. If the argument is a vector then the
corresponding symbol is vector_selector.
It is important to note as well the order of arguments. The MathML
<selector/> tag first takes the vector or matrix object, and
then the indices of selection. In OpenMath it is the other way around.
First the indices of selection are given and then the object.
Another element where differences in structure are important is the
matrix element. OpenMath has two ways of representing matrices. One
representation defined in the "linalg1" CD and the other defined
in the "linalg2" CD. A matrix is defined as a series of
matrixrows in "linalg1", exactly as in MathML. For such
matrices, translation is straightforward.
However, "linalg2" defines a matrix as a series of matrix
columns. This representation has no equivalent in MathML. It is
important that a translator is capable of understanding both
representations in order to offer correct translation.
When dealing with a "linalg2" matrix, a procedure can be
implemented which given the matrix columns of a matrix, returns a
series of matrix rows representing the same matrix. From these matrix
rows, a MathML expression can be generated.